Question

Using the information given in the following figure, find $AB$.

Answer 1

According to Sine's law:
$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
$\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}$ ....(i)
Now, $\angle A={60}^o,\angle B={90}^o,\angle C={30}^o$
From (i), we have

$\frac{AC}{\sin B}=\frac{AB}{\sin C}$
$\Rightarrow \frac{10}{\sin {90}^o}=\frac{AB}{\sin {30}^o}$
$\Rightarrow AB=10\times \sin {30}^o$
$\Rightarrow AB=10\times 0.5=5cm$